300edo - Revision history

ArrowHead294 at 22:38, 20 February 2025

2025-02-20T22:38:45Z

← Older revision		Revision as of 22:38, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	300edo's step size is called a '''savart''' when used as an [[interval size unit]].		300edo's step size is called a '''savart''' when used as an [[interval size unit]].

FloraC: /* Theory */ cleanup

2025-01-17T15:51:38Z

Theory: cleanup

← Older revision		Revision as of 15:51, 17 January 2025
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	== Theory ==		== Theory ==
	300edo is the largest-number edo which [[tempers out]] the [[Pythagorean comma]], 531441/524288, in the [[patent val]].		300edo is the largest-number edo which [[tempering out\|tempers out]] the [[Pythagorean comma]], 531441/524288, in the [[patent val]].

	It is in[[consistent]] to the [[5-odd-limit]] and higher, with three mappings possible for the 5-limit: {{val\| 300 475 697 }} (patent val), {{val\| 300 '''476''' 697 }} (300b), and {{val\| 300 475 '''696''' }} (300c).		It is in[[consistent]] to the [[5-odd-limit]] and higher, with three mappings possible for the 5-limit: {{val\| 300 475 697 }} (patent val), {{val\| 300 '''476''' 697 }} (300b), and {{val\| 300 475 '''696''' }} (300c).
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 300 factors into ~~{{factorization\|300}}~~, 300edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150 }}. [[600edo]], which doubles it, gives a good correction to its approximation of the 5-limit.		Since 300 factors into 2<sup>2</sup> × 3 × 5<sup>2</sup>, 300edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150 }}. [[600edo]], which doubles it, gives a good correction to its approximation of the 5-limit.

	== External links ==		== External links ==
	* [http://tonalsoft.com/enc/s/savart.aspx savart] on [[Tonalsoft Encyclopedia]]		* [http://tonalsoft.com/enc/s/savart.aspx savart] on [[Tonalsoft Encyclopedia]]

Fredg999: Mention "savart" (name for step size), external link, misc. edits

2024-07-01T01:58:13Z

Mention "savart" (name for step size), external link, misc. edits

← Older revision		Revision as of 01:58, 1 July 2024
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	{{EDO intro}}		{{EDO intro}}

	300edo is the largest-number edo which [[~~tempering out\|~~tempers out]] the [[~~pythagorean~~ comma]], 531441/524288, in the [[patent val]].		300edo's step size is called a '''savart''' when used as an [[interval size unit]].

			== Theory ==
			300edo is the largest-number edo which [[tempers out]] the [[Pythagorean comma]], 531441/524288, in the [[patent val]].

	It is in[[consistent]] to the [[5-odd-limit]] and higher, with three mappings possible for the 5-limit: {{val\| 300 475 697 }} (patent val), {{val\| 300 '''476''' 697 }} (300b), and {{val\| 300 475 '''696''' }} (300c).		It is in[[consistent]] to the [[5-odd-limit]] and higher, with three mappings possible for the 5-limit: {{val\| 300 475 697 }} (patent val), {{val\| 300 '''476''' 697 }} (300b), and {{val\| 300 475 '''696''' }} (300c).
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 300 factors into {{factorization\|300}}, 300edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150 }}. [[600edo]], which doubles it, gives a good correction to its approximation of the 5-limit.		Since 300 factors into {{factorization\|300}}, 300edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150 }}. [[600edo]], which doubles it, gives a good correction to its approximation of the 5-limit.

			== External links ==
			* [http://tonalsoft.com/enc/s/savart.aspx savart] on [[Tonalsoft Encyclopedia]]

FloraC: Cleanup and +subsets and supersets

2024-03-01T03:56:29Z

Cleanup and +subsets and supersets

← Older revision		Revision as of 03:56, 1 March 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''300edo''' is the [[~~EDO~~\|equal division of the octave]] into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288.~~		{{EDO intro}}

	It is ~~inconsistent to~~ the 5-~~limit and higher limit~~, ~~with three mappings possible for~~ the ~~5-limit: <300 475 697\| (~~patent val~~), <300 476 697\| (300b), and <300 475 696\| (300c)~~.		300edo is the largest-number edo which [[tempering out\|tempers out]] the [[pythagorean comma]], 531441/524288, in the [[patent val]].

	~~Using~~ the ~~patent val~~, ~~it tempers out 531441/524288 and \|47 7 -25> in~~ the 5-limit~~; 6144/6125~~, ~~50421/50000~~, and ~~1594323/1568000 in the 7-limit~~.		It is in[[consistent]] to the [[5-odd-limit]] and higher, with three mappings possible for the 5-limit: {{val\| 300 475 697 }} (patent val), {{val\| 300 '''476''' 697 }} (300b), and {{val\| 300 475 '''696''' }} (300c).

	Using the ~~300b~~ val, it tempers out ~~393216~~/~~390625~~ and \|51 -~~38 4>~~ in the 5-limit; ~~153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976~~/~~10935~~, ~~65536~~/~~64827~~, and ~~390625~~/~~388962~~ in the 7-limit.		Using the patent val, it tempers out 531441/524288 and {{monzo\| 47 7 -25 }} in the 5-limit; [[6144/6125]], [[50421/50000]], and 1594323/1568000 in the 7-limit.

	Using the ~~300c~~ val, it tempers out ~~531441~~/~~524288~~ and \|-~~58 0 25>~~ in the 5-limit; ~~225~~/~~224~~, ~~250047~~/~~250000~~, and ~~69206436005~~/~~68719476736~~ in the 7-limit.		Using the 300b val, it tempers out [[393216/390625]] and {{monzo\| 51 -38 4 }} in the 5-limit; 153664/151875, 179200/177147, and [[823543/819200]] in the 7-limit. Using the 300bd val, it tempers out [[10976/10935]], 65536/64827, and [[390625/388962]] in the 7-limit.

			Using the 300c val, it tempers out 531441/524288 and {{monzo\| -58 0 25 }} in the 5-limit; [[225/224]], [[250047/250000]], and 69206436005/68719476736 in the 7-limit.

			=== Odd harmonics ===
	{{Harmonics in equal\|300}}		{{Harmonics in equal\|300}}
	[[~~Category:Equal divisions~~ of the ~~octave\|###]] <!-- 3-digit number -~~->
			=== Subsets and supersets ===
			Since 300 factors into {{factorization\|300}}, 300edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150 }}. [[600edo]], which doubles it, gives a good correction to its approximation of the 5-limit.

BudjarnLambeth: Added "harmonics in equal" table

2023-06-24T07:12:08Z

Added "harmonics in equal" table

← Older revision		Revision as of 07:12, 24 June 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''300edo''' is the [[EDO\|equal division of the octave]] into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697\| (patent val), <300 476 697\| (300b), and <300 475 696\| (300c). Using the patent val, it tempers out 531441/524288 and \|47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and \|51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and \|-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.		'''300edo''' is the [[EDO\|equal division of the octave]] into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288.

			It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697\| (patent val), <300 476 697\| (300b), and <300 475 696\| (300c).

			Using the patent val, it tempers out 531441/524288 and \|47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit.

			Using the 300b val, it tempers out 393216/390625 and \|51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit.

			Using the 300c val, it tempers out 531441/524288 and \|-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.

			{{Harmonics in equal\|300}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:48:39Z

Infobox ET added

← Older revision		Revision as of 21:48, 4 October 2022
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			{{Infobox ET}}
	'''300edo''' is the [[EDO\|equal division of the octave]] into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697\| (patent val), <300 476 697\| (300b), and <300 475 696\| (300c). Using the patent val, it tempers out 531441/524288 and \|47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and \|51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and \|-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.		'''300edo''' is the [[EDO\|equal division of the octave]] into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697\| (patent val), <300 476 697\| (300b), and <300 475 696\| (300c). Using the patent val, it tempers out 531441/524288 and \|47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and \|51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and \|-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Fredg999 category edits: Sort key

2022-07-03T19:14:22Z

Sort key

← Older revision		Revision as of 19:14, 3 July 2022
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	'''300edo''' is the [[EDO\|equal division of the octave]] into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697\| (patent val), <300 476 697\| (300b), and <300 475 696\| (300c). Using the patent val, it tempers out 531441/524288 and \|47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and \|51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and \|-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.		'''300edo''' is the [[EDO\|equal division of the octave]] into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697\| (patent val), <300 476 697\| (300b), and <300 475 696\| (300c). Using the patent val, it tempers out 531441/524288 and \|47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and \|51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and \|-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Keenan Pepper category edits: Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

2020-12-04T23:13:24Z

Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

← Older revision		Revision as of 23:13, 4 December 2020
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	'''300edo''' is the [[EDO\|equal division of the octave]] into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697\| (patent val), <300 476 697\| (300b), and <300 475 696\| (300c). Using the patent val, it tempers out 531441/524288 and \|47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and \|51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and \|-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.		'''300edo''' is the [[EDO\|equal division of the octave]] into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697\| (patent val), <300 476 697\| (300b), and <300 475 696\| (300c). Using the patent val, it tempers out 531441/524288 and \|47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and \|51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and \|-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.

	[[Category:~~Edo~~]]		[[Category:Equal divisions of the octave]]

Moremajorthanmajor at 18:50, 26 March 2019

2019-03-26T18:50:12Z

← Older revision		Revision as of 18:50, 26 March 2019
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	'''300edo''' is the [[EDO\|equal division of the octave]] into 300 parts of ~~exact~~ 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697\| (patent val), <300 476 697\| (300b), and <300 475 696\| (300c). Using the patent val, it tempers out 531441/524288 and \|47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and \|51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and \|-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.		'''300edo''' is the [[EDO\|equal division of the octave]] into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697\| (patent val), <300 476 697\| (300b), and <300 475 696\| (300c). Using the patent val, it tempers out 531441/524288 and \|47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and \|51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and \|-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.

	[[Category:Edo]]		[[Category:Edo]]

Xenllium: Created page with "'''300edo''' is the equal division of the octave into 300 parts of exact 4 cents each. It is the largest number EDO which tempers out the pythagorean comma, 531441..."

2019-03-26T11:18:32Z

Created page with "'''300edo''' is the equal division of the octave into 300 parts of exact 4 cents each. It is the largest number EDO which tempers out the pythagorean comma, 531441..."

New page

'''300edo''' is the [[EDO|equal division of the octave]] into 300 parts of exact 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697| (patent val), <300 476 697| (300b), and <300 475 696| (300c). Using the patent val, it tempers out 531441/524288 and |47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and |51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and |-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.

[[Category:Edo]]

← Older revision		Revision as of 03:56, 1 March 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''300edo''' is the [[~~EDO~~\|equal division of the octave]] into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288.~~		{{EDO intro}}

	It is ~~inconsistent to~~ the 5-~~limit and higher limit~~, ~~with three mappings possible for~~ the ~~5-limit: <300 475 697\| (~~patent val~~), <300 476 697\| (300b), and <300 475 696\| (300c)~~.		300edo is the largest-number edo which [[tempering out\|tempers out]] the [[pythagorean comma]], 531441/524288, in the [[patent val]].

	~~Using~~ the ~~patent val~~, ~~it tempers out 531441/524288 and \|47 7 -25> in~~ the 5-limit~~; 6144/6125~~, ~~50421/50000~~, and ~~1594323/1568000 in the 7-limit~~.		It is in[[consistent]] to the [[5-odd-limit]] and higher, with three mappings possible for the 5-limit: {{val\| 300 475 697 }} (patent val), {{val\| 300 '''476''' 697 }} (300b), and {{val\| 300 475 '''696''' }} (300c).

	Using the ~~300b~~ val, it tempers out ~~393216~~/~~390625~~ and \|51 -~~38 4>~~ in the 5-limit; ~~153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976~~/~~10935~~, ~~65536~~/~~64827~~, and ~~390625~~/~~388962~~ in the 7-limit.		Using the patent val, it tempers out 531441/524288 and {{monzo\| 47 7 -25 }} in the 5-limit; [[6144/6125]], [[50421/50000]], and 1594323/1568000 in the 7-limit.

	Using the ~~300c~~ val, it tempers out ~~531441~~/~~524288~~ and \|-~~58 0 25>~~ in the 5-limit; ~~225~~/~~224~~, ~~250047~~/~~250000~~, and ~~69206436005~~/~~68719476736~~ in the 7-limit.		Using the 300b val, it tempers out [[393216/390625]] and {{monzo\| 51 -38 4 }} in the 5-limit; 153664/151875, 179200/177147, and [[823543/819200]] in the 7-limit. Using the 300bd val, it tempers out [[10976/10935]], 65536/64827, and [[390625/388962]] in the 7-limit.

			Using the 300c val, it tempers out 531441/524288 and {{monzo\| -58 0 25 }} in the 5-limit; [[225/224]], [[250047/250000]], and 69206436005/68719476736 in the 7-limit.

			=== Odd harmonics ===
	{{Harmonics in equal\|300}}		{{Harmonics in equal\|300}}
	[[~~Category:Equal divisions~~ of the ~~octave\|###]] <!-- 3-digit number -~~->
			=== Subsets and supersets ===
			Since 300 factors into {{factorization\|300}}, 300edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150 }}. [[600edo]], which doubles it, gives a good correction to its approximation of the 5-limit.